A bound on the degree of singular vectors for the exceptional Lie superalgebra E(5,10)

2020/06/29 by Daniele Brilli, Brilli, Daniele
Mathematics · Physics and Astronomy · #Advanced Topics in Algebra #Algebraic structures and combinatorial models #FOS: Mathematics #Nonlinear Waves and Solitons #Representation Theory (math.RT)

paper · pdf · doi:10.48550/arxiv.2006.16196

openalex publication_date 2020/06/29 · openalex created_date 2020/07/02 · openalex updated_date 2026/07/28

Abstract

We use the language of Lie pseudoalgebras to gain information about the representation theory of the simple infinite-dimensional linearly compact Lie superalgebra of exceptional type E(5,10). This technology allows us to prove that the degree of singular vectors in minimal Verma modules is ≤ 14. A few technical adjustments allow us to refine the bound, proving that the degree must always be ≤ 12 and it is actually, except for a finite number of cases, ≤ 10.

Citations

• Morphisms of Verma modules over exceptional Lie superalgebra E(5,10)
• Irreducible modules over finite simple Lie pseudoalgebras IV.\n Non-primitive pseudoalgebras

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• Singular vector formulas for Verma modules of simple Lie superalgebras
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